Free Vibration Analysis of Orthotropic Rectangular Plates with Tapered Varying Thickness and Winkler Spring Foundation

Abstract

In this paper, free vibrations of nonuniform rectangular plates varying in one or two directions are investigated. The plate is orthotropic and resting upon a Winkler-type spring foundation. A set of admissible functions which are the static solutions of the tapered beam under arbitrary static load is adopted. By adopting Galerkin's method, the fourth-order differential equation governing the motion of such plates can be solved. The effects of the spring foundation together with the orthotropy aspect ratio, truncation factor, and thickness variation on the natural frequencies of the plate are investigated and discussed. Some results from the present study are compared with those from other literatures.

Keywords:

• Galerkin's method
• Nonuniform plate
• Orthotropic plate
• Tapered beam function
• Winkler-type elastic foundation

ACKNOWLEDGMENT

This research was partially supported by the National Science Council in Taiwan through Grant NSC-97-2815-C-327-013-E. The authors are grateful for this support.

^#Communicated by M. Amabili.